Typical solution time for a vertex-covering algorithm on finite-connectivity random graphs

被引：44

作者：

Weigt, M ^{[1
]}

Hartmann, AK ^{[1
]}

机构：

[1] Univ Gottingen, Inst Theoret Phys, D-37073 Gottingen, Germany

来源：

PHYSICAL REVIEW LETTERS | 2001年 / 86卷 / 08期

关键词：

D O I：

10.1103/PhysRevLett.86.1658

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We analytically describe the typical solution time needed by a backtracking algorithm to solve the vertex-cover problem on finite-connectivity random graphs. We find two different transitions: The first one is algorithm dependent and marks the dynamical transition from linear to exponential solution times. The second one gives the maximum computational complexity, and is found exactly at the threshold where the system undergoes an algorithm-independent phase transition in its solvability. Analytical results are corroborated by numerical simulations.

引用

页码：1658 / 1661

页数：4

共 50 条

[21] Mixing time of vertex-weighted exponential random graphs
DeMuse, Ryan
Easlick, Terry
Yin, Mei
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2019, 362 : 443 - 459
[22] ACQUAINTANCE TIME OF RANDOM GRAPHS NEAR CONNECTIVITY THRESHOLD
Dudek, Andrzej
Pralat, Pawel
SIAM JOURNAL ON DISCRETE MATHEMATICS, 2016, 30 (01) : 555 - 568
[23] Acquaintance time of random graphs near connectivity threshold
Department of Mathematics, Western Michigan University, Kalamazoo
MI
49008, United States
不详
ON, Canada
SIAM J Discrete Math, 1600, 1 (555-568):
[24] A linear time algorithm for bi-connectivity augmentation of graphs with upper bounds on vertex-degree increase
Fukuoka, T
Mashima, T
Taoka, S
Watanabe, T
IEICE TRANSACTIONS ON FUNDAMENTALS OF ELECTRONICS COMMUNICATIONS AND COMPUTER SCIENCES, 2005, E88A (04): : 954 - 963
[25] A polynomial algorithm determining cyclic vertex connectivity of 4-regular graphs
Jun Liang
Dingjun Lou
Zongrong Qin
Qinglin Yu
Journal of Combinatorial Optimization, 2019, 38 : 589 - 607
[26] Algorithm for Adjacent Vertex Sum Reducible Edge Coloring of Random Graphs
Li, Jingwen
Zh, Shucheng
Luo, Rong
Lan, Linyu
ENGINEERING LETTERS, 2022, 30 (02) : 730 - 736
[27] A polynomial algorithm determining cyclic vertex connectivity of 4-regular graphs
Liang, Jun
Lou, Dingjun
Qin, Zongrong
Yu, Qinglin
JOURNAL OF COMBINATORIAL OPTIMIZATION, 2019, 38 (02) : 589 - 607
[28] Dynamical replica analysis of processes on finitely connected random graphs: I. Vertex covering
Mozeika, A.
Coolen, A. C. C.
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2008, 41 (11)
[29] Thermodynamic construction of a one-step replica-symmetry-breaking solution in finite-connectivity spin glasses
Nakajima, T.
Hukushima, K.
PHYSICAL REVIEW E, 2009, 80 (01):
[30] Analysis of an iterated local search algorithm for vertex cover in sparse random graphs
Witt, Carsten
THEORETICAL COMPUTER SCIENCE, 2012, 425 : 117 - 125

← 1 2 3 4 5 →